This question is far too broad. If you would like to address individual aspects of Modernism and its impact on Europe post World War I, please ask each portion as a separate question.
Here I will focus on how Modernism affected architecture in Europe in the post war period.
In Germany, Bauhaus gathered a group of professors to work together to create affordable mass housing. Such structures were needed to replace the massive losses incurred during the war.
In Holland, the focus was not on mass production but on the spiritual. Architects, such as Theo van Doesburg and Gerrit Rietveld created pyramid housing and used a variety of colors.
In France, Le Corbusier focused on urban planning based on his “five principles of modern architecture." Le Corbusier thought of the home as a machine that could advance living, a very modernist concept.
In Italy, Giuseppe Terragni, although a fascist, had the same ideas about modernist architecture as did his leftist counterparts. He believed, as did they, that the new age demanded a break from the past, and the functionality needed to be optimized for collective living.